In this section we study the case in which the family frequencies of the GWF model
are constructed from a size-biased pick
\((\tilde{V}_1, \tilde{V}_2,\dots )\)  of a Poisson-Dirichlet (PD) random mass partition of parameters
\((\alpha ,\theta )\) , \(0<\alpha <1, \theta >-\alpha \)  ([1]}), by setting
\(\eta ^{(N)}_i = \frac{\tilde{V}_{i}^\gamma }{\sum _{j=1}^N \tilde{V}_j^\gamma }, \quad 1\le i \le N,\) 
